Defining parameters
Level: | \( N \) | \(=\) | \( 3600 = 2^{4} \cdot 3^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 3600.e (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 4 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 4 \) | ||
Sturm bound: | \(720\) | ||
Trace bound: | \(13\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(3600, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 90 | 6 | 84 |
Cusp forms | 18 | 6 | 12 |
Eisenstein series | 72 | 0 | 72 |
The following table gives the dimensions of subspaces with specified projective image type.
\(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
---|---|---|---|---|
Dimension | 6 | 0 | 0 | 0 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(3600, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | Image | CM | RM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||||
3600.1.e.a | $1$ | $1.797$ | \(\Q\) | $D_{2}$ | \(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-5}) \) | \(\Q(\sqrt{5}) \) | \(0\) | \(0\) | \(0\) | \(0\) | \(q+2q^{29}+2q^{41}+q^{49}-2q^{61}+2q^{89}+\cdots\) |
3600.1.e.b | $1$ | $1.797$ | \(\Q\) | $D_{2}$ | \(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-1}) \) | \(\Q(\sqrt{3}) \) | \(0\) | \(0\) | \(0\) | \(0\) | \(q+2q^{13}-2q^{37}+q^{49}+2q^{61}+2q^{73}+\cdots\) |
3600.1.e.c | $2$ | $1.797$ | \(\Q(\sqrt{-3}) \) | $D_{6}$ | \(\Q(\sqrt{-3}) \) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+(\zeta_{6}+\zeta_{6}^{2})q^{7}-q^{13}+(\zeta_{6}+\zeta_{6}^{2}+\cdots)q^{19}+\cdots\) |
3600.1.e.d | $2$ | $1.797$ | \(\Q(\sqrt{-3}) \) | $D_{6}$ | \(\Q(\sqrt{-3}) \) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+(-\zeta_{6}-\zeta_{6}^{2})q^{7}+q^{13}+(\zeta_{6}+\zeta_{6}^{2}+\cdots)q^{19}+\cdots\) |
Decomposition of \(S_{1}^{\mathrm{old}}(3600, [\chi])\) into lower level spaces
\( S_{1}^{\mathrm{old}}(3600, [\chi]) \simeq \) \(S_{1}^{\mathrm{new}}(144, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(400, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(900, [\chi])\)\(^{\oplus 3}\)